Question

In the following table, Laspeyre's and Paasche's Price Index Numbers are equal. Complete the following activity to find x :

Commodity	Base Year		Current year
	Price	Quantity	Price	Quantity
A	2	10	2	5
B	2	5	x	2

Solution: P₀₁(L) = P₀₁(P)

`(sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = square/(sum "p"_0"q"_1) xx 100`

`(20 + 5x)/square xx 100 = square/14 xx 100`

∴ x = `square`

Answer 1

Commodity	Base Year		Current year		p0q0	p1q0	p0q1	p1q1
	p0	q0	p1	q1
A	2	10	2	5	20	20	10	10
B	2	5	x	2	10	5x	4	2x
Total	-	-	-	-	30	20+5x	14	10+2x

P₀₁(L) = P₀₁(P)

`(sum "p"_1"q"_0)/(sum "p"_0"q"_0) xx 100 = bb(sum "p"_1"q"_1)/(sum "p"_0"q"_1) xx 100`

`(20 + 5x)/bb30 xx 100 = bb(10 + 2x)/14 xx 100`

∴ `280 + 70x = 300 + 60x`

∴ `10x = 20`

∴ x = 2